Problem: Express this product in scientific notation: $(4.50\times 10^{5})\times (5.00\times 10^{-1})$
Answer: Start by collecting like terms together. $= (4.50\times 5.00) \times (10^{5}\times 10^{-1})$ When multiplying exponents with the same base, add the powers together. $= 22.5 \times 10^{5\,+\,-1}$ $= 22.5 \times 10^{4}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the left without changing the value of our answer. $ $ We can use the fact that $22.5$ is the same as $2.250 \times 10$ $ = {2.250 \times 10} \times 10^{4} $ $= 2.250\times 10^{5}$